A: (0.75, 1.5)
B: (-1.25, -0.5)
C: (2, 0)
a = Segment(B, C)
b = Segment(C, A)
c = Segment(A, B)
s1: a^(2) + b^(2) + c^(2)
s3: (((a * b) * c))^(2)
s2: ((a * b))^(2) + ((c * a))^(2) + ((b * c))^(2)
sq: (16 * Area[A, B, C]^(2))
f(x) = (3 * x^(5)) - ((9 * s1) * x^(4)) + ((2 * ((3 * s1^(2)) + (4 * s2))) * x^(3)) + ((2 * ((3 * s1^(3)) - ((20 * s1) * s2) + (48 * s3))) * x^(2)) + ((sq * ((9 * s1^(2)) - (20 * s2))) * x) - (sq * ((3 * s1^(3)) - ((12 * s1) * s2) + (32 * s3)))
w = Root(f)
vv(a, b, c) = ((x(w))^(2) - ((2 * (b^(2) + c^(2) - a^(2))) * x(w)) - ((3 * a^(4)) - ((2 * a^(2)) * b^(2)) - ((2 * a^(2)) * c^(2)) - b^(4) + ((2 * b^(2)) * c^(2)) - c^(4))) / ((3 * (x(w))^(2)) - ((2 * s1) * x(w)) + sq)
X = Barycenter({A, B, C}, {vv(a, b, c), vv(b, c, a), vv(c, a, b)})
ω: atand((4 * Area[A, B, C] / x(w)))
xa = Distance(X, A)
xb = Distance(X, B)
xc = Distance(X, C)
R_A = Barycenter({X, B, C}, {1 / xc^(2), 1 / xb^(2), 1 / a^(2)})
R_B = Barycenter({A, X, C}, {1 / b^(2), 1 / xa^(2), 1 / xc^(2)})
R_C = Barycenter({A, B, X}, {1 / xa^(2), 1 / c^(2), 1 / xb^(2)})
ω_A = Angle(B, X, R_A)
ω_C = Angle(A, X, R_C)
ω_B = Angle(C, X, R_B)
XA = Segment(X, A)
XB = Segment(X, B)
XC = Segment(X, C)
text1: "ω_A=" + ω_A + "
ω_B=" + ω_B + "
ω_C=" + ω_C + "
ω=" + ω + ""